# Combinations of samples problem

1. Jul 29, 2014

### jonroberts74

1. The problem statement, all variables and given/known data

Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.
a. How many different samples can be chosen?
b. How many samples will contain at least one defective board?
c. What is the probability that a randomly chosen sample of five contains at least one defective board?

3. The attempt at a solution

A) $\binom{40}{5} = \frac{40!}{5!(35!)} = 658\;008$

B) $\binom{5}{1}+\binom{5}{2}+\binom{5}{3} = 25$

C) $P(E) = \frac{N(E)}{N(S)} = \frac{25}{658\;008}$

2. Jul 30, 2014

### jonroberts74

B) $\binom{3}{1}\binom{37}{4}+\binom{3}{2}\binom{37}{3}+\binom{3}{3} \binom{37}{2} = 222\,111$

C) $P(E) = \frac{N(E)}{N(S)} = \frac{222\,111}{658\,008} \approx 33.76\%$

3. Jul 30, 2014

### vela

Staff Emeritus
Your second attempt looks good.

Another way to calculate (B) is to figure out how many ways to select 5 good boards and then subtract that number from your answer to (A).

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted